As shown in the figure, the wheel with radius \( R=5 \mathrm{~cm} \) rotates about \( O \) driven by the block hanging onto the cord around it. The position equation of the block is \( x=0.2 t^{2} \), wherein \( x \) is measured in \( \mathrm{m} \) and \( t \) is in s. Find the magnitude of the acceleration of a particle on the rim of the wheel, expressed as a function of \( x \).
Added by Dji S.
Close
Step 1
First, we need to find the velocity of the block as a function of time. To do this, we can differentiate the position equation with respect to time: \(v = \frac{dx}{dt} = 0.4t\) Show more…
Show all steps
Your feedback will help us improve your experience
Dave Kratz and 62 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A wheel of radius $0.20 \mathrm{~m}$ is mounted on a frictionless horizontal axis. The rotational inertia of the wheel about the axis is $0.050 \mathrm{~kg} \cdot \mathrm{m}^{2}$. A massless cord wrapped around the wheel is attached to a $2.0 \mathrm{~kg}$ block that slides on a horizontal frictionless surface. If a horizontal force of magnitude $P=3.0 \mathrm{~N}$ is applied to the block as shown in Fig. $10-56$, what is the magnitude of the angular acceleration of the wheel? Assume the cord does not slip on the wheel.
SSM A wheel of radius 0.20 $\mathrm{m}$ is mounted on a frictionless horizon- tal axis. The rotational inertia of the wheel about the axis is 0.050 $\mathrm{kg} \cdot \mathrm{m}^{2}$ . A massless cord wrapped around the wheel is attached to a 2.0 $\mathrm{kg}$ block that slides on a horizontal frictionless surface. If a horizontal force of magnitude $P=3.0 \mathrm{N}$ is applied to the block as shown in Fig. $10-56$ , what is the magnitude of the angular acceleration of the wheel? Assume the cord does not slip on the wheel.
$\textbf{Figure P10.59}$ illustrates an Atwood's machine. Find the linear accelerations of blocks $A$ and $B$, the angular acceleration of the wheel $C$, and the tension in each side of the cord if there is no slipping between the cord and the surface of the wheel. Let the masses of blocks $A$ and $B$ be 4.00 kg and 2.00 kg, respectively, the moment of inertia of the wheel about its axis be 0.220 kg $\cdot$ m$^2$, and the radius of the wheel be 0.120 m. Figure P10.59 (CAN'T COPY THE FIGURE)
Dynamics of Rotational Motion
Gyroscopes and Precession
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Watch the video solution with this free unlock.
EMAIL
PASSWORD